Image-forming MR methods which utilize the interaction between magnetic fields and nuclear spins in order to form two-dimensional or three-dimensional images are widely used nowadays, notably in the field of medical diagnostics, because for the imaging of soft tissue they are superior to other imaging methods in many respects, do not require ionizing radiation and are usually not invasive.
According to the MR method in general, the body of the patient to be examined is arranged in a strong, uniform magnetic field (B0 field) whose direction at the same time defines an axis (normally the z-axis) of the co-ordinate system on which the measurement is based. The magnetic field splits different energy levels for the individual nuclear spins in dependence on the magnetic field strength and the specific spin properties. The spin system can be excited (spin resonance) by application of an electromagnetic alternating field (RF field, also referred to as B1 field) of defined frequency (so-called Larmor frequency, or MR frequency). From a macroscopic point of view the distribution of the individual nuclear spins produces an overall magnetization which can be deflected out of the state of equilibrium by application of an electromagnetic pulse of appropriate radio frequency (RF pulse) while the corresponding B1 magnetic field extends perpendicular to the z-axis, so that the magnetization performs a precessional motion about the z-axis. The precessional motion describes a surface of a cone whose angle of aperture is referred to as flip angle. The magnitude of the flip angle is dependent on the strength and the duration of the applied electromagnetic RF pulse. In the case of a so-called 90° pulse, the spins are deflected from the z axis to the transverse plane (flip angle 90°).
After termination of the RF pulse, the magnetization relaxes back to the original state of equilibrium, in which the magnetization in the z direction is built up again with a first time constant T1 (spin lattice or longitudinal relaxation time), and the magnetization in the direction perpendicular to the z direction relaxes with a second time constant T2 (spin-spin or transverse relaxation time). The variation of the magnetization can be detected by means of one or more receiving RF coils which are arranged and oriented within an examination volume of the MR device in such a manner that the variation of the magnetization is measured in the direction perpendicular to the z-axis. The decay of the transverse magnetization is accompanied, after application of, for example, a 90° RF pulse, by a transition of the nuclear spins (induced by local magnetic field inhomogeneities) from an ordered state with the same phase to a state in which all phase angles are uniformly distributed (dephasing). The dephasing can be compensated by means of a refocusing pulse (for example a 180° pulse). This produces an echo signal (spin echo) in the receiving coils.
In order to realize spatial resolution in the body, linear magnetic field gradients extending along the three main axes are superposed on the uniform magnetic field, leading to a linear spatial dependency of the spin resonance frequency. The signal picked up in the receiving coils then contains components of different frequencies which can be associated with different locations in the body. The MR signal data obtained via the RF coils corresponds to the spatial frequency domain and is called k-space data. The k-space data are usually acquired along multiple lines with different phase encoding values to achieve sufficient coverage. Each line is digitized during read-out by collecting a number of samples. A set of k-space data is converted to a MR image by means of Fourier transformation.
Echo planar imaging (EPI) is a known rapid MR imaging technique which is used to produce MR images at high acquisition rates, typically several images per second. It has been found particularly useful in diffusion imaging, for functional magnetic resonance imaging (fMRI), in dynamic imaging etc. The basic idea of EPI is to completely sample k-space in a single repetition (single-shot EPI) during one T2 decay, or in multiple shots (multi-shot EPI). In single-shot EPI, all k-space lines are acquired during multiple magnetic field gradient reversals, producing multiple gradient echo signals in a single acquisition after a single RF excitation pulse, i.e., in a single measurement or “shot”. In multi-shot EPI, the acquisition of MR signals is divided into multiple shots. In this case, k-space is segmented by multiple acquisitions. Multi-shot EPI is also referred to as segmental EPI.
MR images reconstructed from EPI acquisitions tend to suffer from so-called “Nyquist ghosting”. In the case of single-shot EPI, the ghost image is shifted by half a field of view in the phase encoding direction. In multi-shot EPI, the ghosting pattern can be more complex. The Nyquist ghost artifacts are caused mainly by induced eddy currents and system timing errors with respect to the positive and negative magnetic field gradient lobes. These errors are associated with the MR scanner hardware.
Several methods are known in the art for correcting the Nyquist ghost artifacts, for example based on information gained from reference scans or navigator echoes acquired together with image data. Reference scans may be employed to determine systematic phase errors of the MR signals induced by the imperfections of magnetic field gradient switching. The imaging data can then be corrected accordingly. Navigator echoes can be used, preferably in dynamic EPI scans, to track the varying delays of magnetic field gradient switching.
A drawback of these known techniques is that the applied corrections are generally not able to completely remove the Nyquist ghosts. This is caused by the magnetic field gradient switching delays changing over time (without being re-estimated correctly), application of only a one-dimensional phase correction (in the phase encoding direction), missing compensation of higher order terms etc.
Other purely “data driven” approaches exist that do not require either a reference scan or navigators (see e.g. Clare, “Iterative Nyquist Ghost Correction for Single and Multi-shot EPI using an Entropy Measure”, Proc. Intl. Soc. Mag. Reson. Med. 11, 2003). A drawback of such techniques is that they tend to require a prohibitively long reconstruction time. The ISMRM abstract ISMRM2007-987(D3) concerns the problem of Nyquist ghosting in single-shot EPI and provides a de-ghosting in the image domain driven by a metric based on coil consistency.